Similar calculations give the diagonal dominance in near-boundary equations which yields the unique solvability of (4.9) in this case.

In general case, there may be no diagonal dominance in equations (4.1).

The matrix A has diagonal dominance in rows which gives its invertibility.

An appropriate precompensator [K.sub.p] is designed to make the system TFM diagonal dominance, that is, to decouple the control plant.

A square matrix Q(s) is said to be of diagonal dominance on a contour D if, for each column (or row), the modulus of the diagonal element is larger than the sum of the modulus of the off-diagonal elements for each complex variable s in D:

When A is an irreducible matrix with weak

diagonal dominance, obviously, both the coefficient matrix A and the corresponding diagonal matrix D are nonsingular.

We also introduce a concept of block diagonal dominance different than that used in [7], [8].

In order to define diagonal dominance for blocks, we need to introduce a measure for the smallness of the off-diagonal blocks or, equivalently, a measure for the largeness of the diagonal blocks.

Input and output scaling are employed simultaneously to further reduce the level of ill conditioning in the system and also to obtain the best diagonal dominance across the frequency range of interest, especially near the system bandwidth.

The Gershgorin diagonal dominance discs were used to assess interaction.

conditioning, diagonal dominance, pivoting strategies, accuracy, singular value decomposition.

We start by showing in Section 2 that diagonal dominance implies very well conditioning of both unit triangular matrices L, U.